Jumping between two solid vertical walls

Anyone got an idea how I can make a jumping mechanic between two vertical walls?

I want the object (a simple sprite) to jump between two walls. And somehow make the jump "bend" upwards.

Kind of hard to explain, so here's an image to help me explain it:

For that ratio, I would use a high max speed, raise the acceleration somewhat, and use low jumping power (Just use high sustain and double jump). Were you trying to ask something else?

Solution: Superpower Sine Waves.

But for upward-bending jumping (Opposite as the diagram shows), I would just add a vertical sine behavior to your player and pause it once the sine reaches its peak, then disable it and set its cycle position to the default. If it goes through the normally solid ceilings, then, well, it could be a cool superpower! :)

(But in that case, you might need a power-up.)